Markov perfect equilibria in a dynamic decision model with quasi-hyperbolic discounting

Łukasz Balbus, Anna Jaśkiewicz and Andrzej Nowak

Annals of Operations Research, 2020, vol. 287, issue 2, No 2, 573-591

Abstract: Abstract We study a discrete-time non-stationary decision model in which the preferences of the decision maker change over time and are described by quasi-hyperbolic discounting. A time-consistent optimal solution in this model corresponds with a Markov perfect equilibrium in a stochastic game with uncountable state space played by countably many short-lived players. We show that Markov perfect equilibria may be constructed using a generalized policy iteration algorithm. This method is in part inspired by the fundamental works of Mertens and Parthasarathy (in: Raghavan, Ferguson, Parthasarathy, Vrieze (eds) Stochastic games and related topics, Kluwer Academic Publishers, Dordrecht, 1991; in: Neyman, Sorin (eds) Stochastic games and applications, Academic Publishers, Dordrecht, 2003) devoted to subgame perfect equilibria in standard n-person discounted stochastic games. If the one-period utilities and transition probabilities are independent of time, we obtain on new existence results on stationary Markov perfect equilibria in the models with unbounded from above utilities.

Keywords: Stochastic game; Uncountable state space; Quasi-hyperbolic discounting; Non-atomic transition probability; Markov perfect equilibrium; 91A13; 91A25; 91B51; 91B62 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-018-2778-2

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